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Demonstratio Mathematica

Editor-in-Chief: Vetro, Calogero


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CiteScore 2018: 0.47
SCImago Journal Rank (SJR) 2018: 0.265
Source Normalized Impact per Paper (SNIP) 2018: 0.714

Mathematical Citation Quotient (MCQ) 2018: 0.17

ICV 2018: 121.16

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ISSN
2391-4661
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Volume 51, Issue 1

Issues

Approximate property of a functional equation with a general involution

Won-Gil Park
  • Corresponding author
  • Department of Mathematics Education, College of Education, Mokwon University, Daejeon, Republic of Korea
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/ Jae-Hyeong Bae
Published Online: 2018-11-20 | DOI: https://doi.org/10.1515/dema-2018-0021

Abstract

In this paper, we prove the Hyers-Ulam stability of the functional equation f(x + y, z + w) + f(x + σ(y),z + τ(w)) = 2f(x, z) + 2f(y, w), where σ, τ are involutions.

Keywords: approximation; involution; Banach space

References

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  • [2] Hyers D. H., On the stability of the linear functional equation, Proc. Nat. Acad. Sci. U.S.A., 1941, 27(4), 222-224CrossrefGoogle Scholar

  • [3] Aczél J., Dhombres J., Functional Equations in Several Variables, Cambridge Univ. Press, Cambridge, 1989CrossrefWeb of ScienceGoogle Scholar

  • [4] Brzdek J., Popa D., Rasa I., Xu B., Ulam Stability of Operators, A volume in Mathematical Analysis and its Applications, Academic Press, Elsevier, Oxford, 2018Google Scholar

  • [5] El-fassi I., Brzdek J., Chahbi A., Kabbaj S., On hyperstability of the biadditive functional equation, ActaMath. Sci. Ser. B, 2017, 37(6), 1727-1739Google Scholar

  • [6] Găvruta P., A generalization of the Hyers-Ulam-Rassias stability of approximately additive mappings, J. Math. Anal. Appl., 1994, 184(3), 431-436Google Scholar

  • [7] Jung S.-M., On the Hyers-Ulam Stability of the functional equations that have the quadratic property, J. Math. Anal. Appl., 1998, 222(1), 126-137Google Scholar

  • [8] Bae J.-H., Park W.-G., A functional equation originating from quadratic forms, J. Math. Anal. Appl., 2007, 326(2), 1142-1148Google Scholar

  • [9] Bae J.-H., Park W.-G., A functional equation originating from additive forms, (submitted).Google Scholar

About the article

Received: 2018-05-17

Accepted: 2018-09-03

Published Online: 2018-11-20

Published in Print: 2018-11-01


Citation Information: Demonstratio Mathematica, Volume 51, Issue 1, Pages 304–308, ISSN (Online) 2391-4661, DOI: https://doi.org/10.1515/dema-2018-0021.

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© by Won-Gil Park, Jae-Hyeong Bae, published by De Gruyter. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License. BY-NC-ND 4.0

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